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If two perpendicular tangents PA and PB are drawn from an external point to a circle of radius 4cm, then the length of each tangent is
Given: - Radius of circle = 4 cm, - Tangents PA and PB are perpendicular. The tangents form a square with the radii. The diagonal of the square is the hypotenuse: Diagonal = √(4² + 4²) = √32 = 4√2. Side (tangent length) = Diagonal / √2 = 4√2 / √2 = 4 cm. This question is associated with Chapter 10 oRead more
Given:
– Radius of circle = 4 cm,
– Tangents PA and PB are perpendicular.
The tangents form a square with the radii. The diagonal of the square is the hypotenuse:
Diagonal = √(4² + 4²) = √32 = 4√2.
Side (tangent length) = Diagonal / √2 = 4√2 / √2 = 4 cm.
This question is associated with Chapter 10 of the Class 10th NCERT Mathematics textbook, which deals with the topic of “Circles.” Answer the question based on your understanding of the concepts covered in this chapter.
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If PA and PB are tangents to the circle with the centre O such that angle APB = 50°, then angle OAB is equal to
We are given: - PA and PB are tangents to the circle with center O, - Angle ∠APB = 50°. Key property of tangents The tangents PA and PB are equally inclined to the line joining the external point P to the center O. Therefore: ∠APO = ∠BPO = ∠APB / 2. Substitute ∠APB = 50°: ∠APO = ∠BPO = 50° / 2 = 25°Read more
We are given:
– PA and PB are tangents to the circle with center O,
– Angle ∠APB = 50°.
Key property of tangents
The tangents PA and PB are equally inclined to the line joining the external point P to the center O. Therefore:
∠APO = ∠BPO = ∠APB / 2.
Substitute ∠APB = 50°:
∠APO = ∠BPO = 50° / 2 = 25°.
Relationship between angles
In triangle OAB:
– OA and OB are radii of the circle, so triangle OAB is isosceles.
– The angle ∠OAB is equal to ∠APO because the tangent PA is perpendicular to the radius OA.
Thus:
∠OAB = ∠APO = 25°.
This question is linked to Chapter 10 of the Class 10th NCERT Mathematics textbook, which is on the topic of “Circles.” Respond with an answer that reflects your understanding of the chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
From a point Q, the length of the tangent to to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
Given: - Length of tangent = 24 cm, - Distance from Q to center = 25 cm. Using Pythagoras theorem: 25² = 24² + r². Simplify: 625 = 576 + r². Solve for r: r² = 49 ⇒ r = 7 cm. This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your unRead more
Given:
– Length of tangent = 24 cm,
– Distance from Q to center = 25 cm.
Using Pythagoras theorem:
25² = 24² + r².
Simplify:
625 = 576 + r².
Solve for r:
r² = 49 ⇒ r = 7 cm.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
In a right angle triangle ABC, right angled at B, BC = 12 cm and AB = 5 cm. The radius of the circle inscribed in the triangle (in cm) is
Given: - AB = 5 cm, BC = 12 cm, AC = 13 cm (using Pythagoras theorem). Radius of incircle: r = (a + b - c) / 2, where a = 5, b = 12, c = 13. Substitute: r = (5 + 12 - 13) / 2 = 4 / 2 = 2 cm. This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer accRead more
Given:
– AB = 5 cm, BC = 12 cm, AC = 13 cm (using Pythagoras theorem).
Radius of incircle:
r = (a + b – c) / 2,
where a = 5, b = 12, c = 13.
Substitute:
r = (5 + 12 – 13) / 2 = 4 / 2 = 2 cm.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If the angle between the ratio of a circle is 100°, then the angle between the tangents at the end of these radii is
We are given: - The angle between the two radii of a circle is 100°. Key property of tangents The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii. Calculate the angRead more
We are given:
– The angle between the two radii of a circle is 100°.
Key property of tangents
The tangents drawn at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii.
Calculate the angle between the tangents
The sum of the angle between the radii and the angle between the tangents is 180° (since they form a quadrilateral with two right angles). Thus:
Angle between tangents = 180° – Angle between radii.
Substitute the given angle between the radii:
Angle between tangents = 180° – 100° = 80°.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/